How to Find the Magnitude of the Vector

By Oxana Fox
Vectors help solve many practical problems, such as the speed of planes in flight.
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A vector is a geometric object that has both length and direction. Vectors play an important role in science as they can represent physical quantities, for example, the velocity of a plane moving at 600 mph in a northeasterly direction. Each vector has coordinates or components, such as “X” and “Y.” A vector also has magnitude, or length, representing the raw "amount" of a measurement. For a velocity vector, for example, the magnitude represents speed. The calculation of the magnitude is based on the Pythagorean Theorem and requires the vector coordinates.

Step 1

Square the coordinate "X" of the vector. For example, if the vector has coordinates (6,-8) then 6^2 = 36.

Step 2

Square the coordinate "Y" of the vector. In this example, (-8)^2 = 64.

Step 3

Add up squares of coordinates. In this example, the sum is 36 + 64 =100.

Step 4

Take the square root of the sum to compute the magnitude of the vector. In this example, the magnitude is square root of 100 that is 10.

About the Author

Oxana Fox is a freelance writer specializing in medicine and treatment, computer software and hardware, digital photography and financial services. She graduated from Moscow Medical College in 1988 with formal training in pediatrics.